Cobordism, Relative Indices and Stein Fillings

2007/05/11 by Charles L. Epstein, Epstein, Charles L.
Mathematics · #32V30 #58G20 #58J32 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #math.AP #math.CV #msc:32V30 #msc:58G20 #msc:58J32

paper · pdf · doi:10.48550/arxiv.0705.1702

arxiv created 2007/05/11 · arxiv updated 2009/12/01

Abstract

In this paper we build on the framework developed in "Subelliptic Boundary Value Problems for the Spin_C Dirac Operator, I, II, III" to obtain a more complete understanding of the gluing properties for indices of boundary value problems for the SpinC-Dirac operator with sub-elliptic boundary conditions. We extend our analytic results for sub-elliptic boundary value problems for the SpinC-Dirac operator, and gluing results for the indices of these boundary problems to SpinC-manifolds with several pseudoconvex (pseudoconcave) boundary components. These results are applied to study Stein fillability for compact, 3-dimensional, contact manifolds.

Related

• Subelliptic Spin_C Dirac operators, I
• Subelliptic Spin_c Dirac operators, III The Atiyah-Weinstein conjecture
• Subelliptic SpinC Dirac Operators, IV Proof of the Relative Index Conjecture
• Tight contact structures on some plumbed 3-manifolds
• A gluing formula for the Z₂-valued index of odd symmetric operators